The same way glasses in restaurants are washed and reused :-)
Another solution is to bring your own cup.
I reuse the same coffee cup every day. Dishwashers are great.
My dad always told me that dishwashers are the things at the end of your arms. I'm guessing that's not what you mean though. However, do you run your dishwasher daily? If you're a single person living alone, that's a lot of dishes!
My two year-old and wife go through plenty of dishes, too.
"My two year-old and wife" != "a single person living alone" in any language I'm familiar with